First appearance of a ghost after a person's death

You might consider apparition. Collins defines it as:

apparition (n.) an appearance, esp of a ghost or ghostlike figure

Wordnik mentions:

apparition (n.) That which appears or becomes visible; an appearance, especially of a remarkable or phenomenal kind.

Ghosts and other post-mortem visitors are occasionally called revenants, from the present participle of French revenir, 'to return' , so the term revenance might be coined for a first (or indeed any) return.

ODO's definition for wraith reads:

a ghost or ghostlike image of someone, especially one seen shortly before or after their death.

You can also consider using spirit, spectre, phantom or phantasm although they aren't necessarily restricted to first appearances.

Edit: I appear to have misread the question a little.

Giselle's "rising from the tomb into a new state of existence" could perhaps be described as a discarnation. The professional sounding U.S. Spiritist Medical Association describes discarnation in the following excerpt:

We, as spiritists also need to differentiate between death and discarnation. Death is a biological phenomenon where the many organs and systems that maintain life collapse, progressively and irreversibly. Discarnation, in turn, is the process of disconnection between the spirit and the physical body, where the spirit gradually frees itself from the magnetic links that tied it to the matter, unleashing the fluidic bonds that united them. Therefore, usually the process of discarnation begins after the biological phenomenon of death. In turn, death is only definitive after the brainstem becomes inactive.

Webster provides a definition and also does so for disembodiment.

I prefer StoneyB's revenance to either of the above.